Elements of Experimental Stress Analysis. Structures and Solid Body Mechanics Division PDF
Preview Elements of Experimental Stress Analysis. Structures and Solid Body Mechanics Division
STRUCTURES AND SOLID BODY MECHANICS DIVISION General Editor B. G. NEAL Other Pergamon Titles of Interest BRITVEC, S. J. The Stability of Elastic Systems CHEUNG, Y. K. Finite Strip Method in Structural Analysis DYM, C. L. Introduction to the Theory of Shells GIBSON, J. E. Linear Elastic Theory of Thin Shells HEARN, E. J. Mechanics of Materials (in SI Units) HERRMANN, G. & Dynamic Response of Structures PERRONNE, N. HEYMAN, J. Beams and Framed Structures, 2nd Edition JAEGER, L. G. Cartesian Tensors in Engineering Science JAEGER, L. G. Elementary Theory of Elastic Plates JOHNS, D. J. Thermal Stress Analysis LIVESLEY, R. K. Matrix Methods of Structural Analysis, 2nd Edition MALLOWS, D. F. & Stress Analysis Problems in SI Units PICKERING, W. J. PARKES, E. W. Braced Frameworks—An Introduction to the Theory of Structures, 2nd Edition ROZVANY, G. I. N. Optimal Design of Flexural Systems— Beams, Grillages, Slabs, Plates and Shells SAADA, A. S. Elasticity : Theory and Applications WARBURTON, G. B. Dynamical Behaviour of Structures, 2nd Edition ELEMENTS OF EXPERIMENTAL STRESS ANALYSIS SI Edition by A. W. HENDRY Ph.D., D.Sc, M.I.C.E., M.I.Struct.E., F.R.S.E. Professor of Civil Engineering, University of Edinburgh PERGAMON PRESS OXFORD NEW YORK TORONTO SYDNEY · PARIS · FRANKFURT U.K. Pergamon Press Ltd., Headington Hill Hall, Oxford OX3 OBW, England U. S. A. Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523, U.S.A. CANADA Pergamon of Canada Ltd., 75 The East Mall, Toronto, Ontario, Canada AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia FRANCE Pergamon Press SARL, 24 rue des Ecoles, 75240 Paris, Cedex 05, France WEST GERMANY Pergamon Press GmbH, 6242 Kronberg- Taunus. Pferdstrasse 1, Federal Republic of Germany Copyright © 1977 Pergamon Press Ltd. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers First edition 1964 Reprinted 1968 SI edition 1977 Reprinted 1977 Library of Congress Catalog Card No. 76-54580 Printed in Great Britain by Biddies Ltd., Guildford, Surrey ISBN 0 08 021301 4 (Hardcover) ISBN 0 08 021300 6 (Flexicover) PREFACE THE object of experimental stress analysis is to deduce the stress conditions in a structural element subjected to some specified loading either by observation of the physical changes brought about in it by the applied loads or by measurements made on a model or analogue. Ever since the principles of mechanics were first applied to engineering problems in the seventeenth century, recourse has been made to experiment as a means of elucidating the behaviour of structures. Early attempts at experimental analysis were inevitably crude by modern standards but, gradually, reliable methods and precise instruments were evolved which made possible detailed and accurate stress determination. Sensitive strain measuring devices were available in the latter part of the nineteenth century, but they were generally too cumbersome for use on small elements and too delicate for use under field conditions. These limitations were eventually overcome but substantial progress in this branch of stress analysis was made only when electrical resistance strain gauges were introduced in the 1930's. Photo-elasticity was known as a possible means of stress analysis from its discovery by Brewster in 1816, but again substantial progress did not take place until well into the twentieth century, in this case because suitable materials were not available until that time. Very few other methods for detailed stress measurement were developed before the 1930's but since then there has been very rapid progress and there are now techniques for the investigation of practically every kind of stress problem. Associated with these techniques is a range of equipment for applying and measuring loads and for vi PREFACE Vil measuring deflections, accelerations and other quantities which may be required for the assessment of stresses in particular cases. As previously suggested, the development of experimental stress analysis depends very much on develop ments in other fields of technology; for example, advances in strain gauge technique are closely tied to instrument technology in general and extension of the scope of photo-elasticity is almost entirely dependent on the emergence of new transparent plastics which happen to have suitable optical properties for this purpose. Those concerned with stress analysis must therefore look beyond the limits of their specialism in order to distinguish new possibilities and improved methods. The purpose of this book is to describe the principles of the more important and widely used techniques and pieces of equipment and, by reference to a number of selected examples, to suggest appropriate applications of these in laboratory and field investigations. Although the examples used to illustrate the various methods of analysis are taken from the field of Civil Engineering, the book will be of use to all under graduate and postgraduate students who require a basic knowledge of experimental stress analysis. It is also hoped that the book may be of use to practising engineers who may be concerned with experimental investigations in one way or another. A book of this size covering such a wide field cannot possibly deal in great detail with any particular topic; a brief biblio graphy has therefore been given at the end of each chapter which should be sufficient to permit the reader to follow up the outline of principles given here in as great depth as may be required. Attention is directed in particular to the publications of the American Society for Experimental Stress Analysis; these include the very comprehensive Handbook of Experi mental Stress Analysis, edited by Hetényi (Wiley, 1953) and the Proceedings of the Society which contain valuable papers on all aspects of the subject. Many papers relating to Experimental Stress Analysis are of course published in the Vili PREFACE journals of various scientific and professional institutions, in the technical press and by many research institutes. These may be traced by reference to publications such as Building Science Abstracts (H.M.S.O., London) and Applied Mechanics Reviews (American Society of Mechanical Engineers). In conclusion, it may be added that although constant reference to books and periodicals is essential, real knowledge of experimental stress analysis can only be obtained by first hand experience in the laboratory. ACKNOWLEDGEMENTS Acknowledgements are due to the following for permission to make use of material from their publications in this text: The Institution of Civil Engineers. The Institution of Structural Engineers. Rocha, M. M., Director, Laboratorio Nacional de Engen- haria Civil, Lisbon. Maihak A.G., Hamburg. Sharpies Engineering Co. (Bamber Bridge) Ltd., Preston. Vili PREFACE journals of various scientific and professional institutions, in the technical press and by many research institutes. These may be traced by reference to publications such as Building Science Abstracts (H.M.S.O., London) and Applied Mechanics Reviews (American Society of Mechanical Engineers). In conclusion, it may be added that although constant reference to books and periodicals is essential, real knowledge of experimental stress analysis can only be obtained by first hand experience in the laboratory. ACKNOWLEDGEMENTS Acknowledgements are due to the following for permission to make use of material from their publications in this text: The Institution of Civil Engineers. The Institution of Structural Engineers. Rocha, M. M., Director, Laboratorio Nacional de Engen- haria Civil, Lisbon. Maihak A.G., Hamburg. Sharpies Engineering Co. (Bamber Bridge) Ltd., Preston. I MODELS, SCALE FACTORS AND MATERIALS MODELS AND SCALE FACTORS WHEN experimental stress analysis techniques are applied in the design of structures or machines, it is usually necessary to employ reduced scale models in the investigations. Further more, it may be inconvenient or impracticable to make the model of the same material as the prototype or again, it may be desirable to use a model material of low elastic modulus in order to obtain easily measurable strains. It is thus essential that we should know the relationship between phenomena observed in a scale model and the corresponding effects in the full sized construction which it represents. It is, of course, necessary that this knowledge should be available at the outset in order that the model may be designed so as to represent correctly the behaviour of the prototype. The problem of scales may be approached in two ways: firstly, by making use of formulae which represent the solution of a simpler problem of the same general type as that being investigated or, alternatively, by determining the required relationship by dimensional analysis. As an example of the first approach, let us suppose that it is required to investigate the behaviour of a particular type of 1 2 ELEMENTS OF EXPERIMENTAL STRESS ANALYSIS beam: suppose that the beam carries some specified loading, as shown in Fig. 1.1. Denoting the load on the prototype and on the model by appropriate subscripts and assuming geometrical similarity and homologous load systems, we can write: Prototype Model Load Wp W m Shear force Fv Fm Shear stress (mean) Fp/A rm/Am p Bending moment k.Wv.Lp kvVmLm Bending stress Mp . y/Ip M y jlm p m m WpLp . W Vm Deflection m hplp W1| W12 1W3 Fig. 1.1. Arbitrary loading on a simple beam. Comparing the various quantities in the prototype and model we may derive the following ratios: Load ratio = shear force ratio : W = W \W r v m F Am __ W Shear stress ratio: v r F ' Ap (L)2 m r rVp L·p Bending moment ratio Wr.Lr Wm Lm Bending stress: EL Lp yp Im __ Wr Wm Lm' ym' Ip ~~ (Lr)2 3 Wp Deflection: ^r · I γ~ I · ^~ · τ = r—Γ W Wm m \Lm/ £<v h ^r · L r MODELS, SCALE FACTORS AND MATERIALS 3 In this way it is possible to determine the relationship between corresponding quantities in the model and prototype and thus to interpret model observations in terms of full size. Examina tion of the relationships for bending stress and deflection show that it is not necessary for the cross section of the model member to be geometrically similar to that of the prototype, provided that the ratio of the moments of inertia is introduced. The final result quoted above of course assumes geometrical similarity throughout. This method can be applied to any problem for which a type solution is known. The alternative approach by dimensional analysis possesses greater generality as knowledge is required only of what variables control the behaviour of the system. It is beyond the scope of this book to deal with the subject of dimensional analysis and only an indication of the method of approach will be attempted; a full treatment of the method will be found in reference 1. If we consider the same problem as discussed above, it is easily seen that the stress in the beam depends only on the loading on it and on its dimensions, i.e. σ oc W*U> (1.1) Now the dimensions of the various terms in (1.1) expressed in fundamental units of force F and length L are: σ [FL-2]; W [F]; L [L] Thus: [FL-η = [F]«[L]b (1.2) Since the equation must be dimensionally homogeneous we may equate indices of like dimensions on the two sides, so that: a= 1 b = -2 This gives: W ace- (1.3)
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